Polygonization of implicit surfaces with constructive solid geometry
Brian Wyvill,Kees van Overveld +1 more
TL;DR: A polygonization algorithm is presented which extends an existing skeletal implicit surface technique to include operations based on Constructive Solid Geometry between blended groups of implicit surface objects, resulting in a surface definition which consists of a boolean expression with union, intersection, and set difference operators.
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Abstract: A polygonization algorithm is presented which extends an existing skeletal implicit surface technique to include operations based on Constructive Solid Geometry between blended groups of implicit surface objects. The result is a surface definition (to be called Boolean Compound Soft Object, or BCSO for short) which consists of a boolean expression with union, intersection, and set difference operators. The geometric primitives that form the operands are soft objects bounded by the iso-surfaces resulting from suitable potential fields. These potential fields are parameterized by configurations of so called skeletal elements. The resulting system, unlike most CSG systems, combines blended and unblended primitives. The polygonization algorithm produces a mesh of triangles to facilitate fast viewing and rendering.
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Figures
Figure 3: Using vector functions to represent several ISM objects at once. 
Figure 8: upper: The Canmore coffee grinder and friends. Lower: American Type 4-4-0 (c. 1855) 15 
Figure 5: Splitting schemes for 3-D triangles 
Figure 7: Combining blended primitives with CSG operations. 
Figure 6: upper: Wheel before and after postprocessing. lower: The Canmore coffee grinder. 
Figure 4: Approximating the intersection of two implicit contours. Left: p12 is a first guess. Right: iterating to get a more accurate approximation of x.
Citations
Extending the CSG Tree. Warping, Blending and Boolean Operations in an Implicit Surface Modeling System
TL;DR: This work describes a hierarchical method which allows arbitrary compositions of models that make use of blending, warping and Boolean operations, called the BlobTree, and presents some examples of interesting models which can be made easily using this approach that would be very difficult to represent with conventional systems.
287
A Survey on Implicit Surface Polygonization
TL;DR: This article presents a survey of different techniques for fast visualization of implicit surfaces, focusing closely on polygonization methods, as they are the most suited to fast visualization.
77
Implicit Blending Revisited
TL;DR: This paper presents a novel, generic solution to blending of functionally‐based implicit surfaces: the insight is that to be intuitive and easy to control, blends should be located where two objects overlap, while enabling other parts of the objects to come as close to each other as desired without being deformed.
Dynamic meshes for accurate polygonization of implicit surfaces with sharp features
Yutaka Ohtake,Alexander Belyaev,Alexander Pasko +2 more
- 07 May 2001
TL;DR: The paper presents a novel approach for accurate polygonization of implicit surfaces with sharp features based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals.
47
Dynamic Mesh Optimization for Polygonized Implicit Surfaces with Sharp Features
TL;DR: A novel approach for accurate polygonization of implicit surfaces with sharp features based on mesh evolution towards a given implicit surface with simultaneous control of the mesh vertex positions and mesh normals is presented.
36
References
Decimation of triangle meshes
William J. Schroeder,Jonathan A. Zarge,William E. Lorensen +2 more
- 01 Jul 1992
TL;DR: An application independent algorithm that uses local operations on geometry and topology to reduce the number of triangles in a triangle mesh and results from two different geometric modeling applications illustrate the strengths of the algorithm.
Representations for Rigid Solids: Theory, Methods, and Systems
TL;DR: A coherent view, based on sound theoretical principles, of what is presently known about the representation of solids is provided by providing a simple mathematical framework for characterizing certain important aspects of representations, for example, their semantic (geometric) integrity.
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An Introduction to Solid Modeling
Martti Mäntylä
- 01 Jun 1988
TL;DR: This is a very reasonable book that should be read as discussed by the authors and the following may offer you the way to get this book: When the other people must walk around and go outside to get the book in the book store, you can just be by visiting this site.
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Data Structure for Soft Objects
TL;DR: A method to represent asoft object, or collection of objects, as a surface of constant value in a scalar field over three dimensions, and its uses in animation are discussed.
Merging BSP trees yields polyhedral set operations
Bruce F. Naylor,John Amanatides,William C. Thibault +2 more
- 01 Sep 1990
TL;DR: In this paper, a distinction is made between the semantics of polyhedra and the more fundamental mechanism of spatial partitioning, and the algorithms required to perform boolean set operations between two objects represented by bsp trees are presented.
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